question_answer

If \[\sin \theta =\frac{8}{17}\] where \[0{}^\circ <\theta <90{}^\circ \], then \[\tan \theta +\sec \theta \] is

A) \[\frac{1}{3}\]

B) \[\frac{2}{3}\]

C) \[\frac{4}{3}\]

D) \[\frac{5}{3}\]

Correct Answer: D

Solution :

\[A{{B}^{2}}=A{{C}^{2}}-B{{C}^{2}}=225\] \[\therefore \]  \[AB=15\] \[\Rightarrow \]               \[\tan \theta =\frac{8}{15}\] and        \[\sec \theta =\frac{17}{15}\] \[\Rightarrow \]               \[\tan \theta +\sec \theta =\frac{5}{3}\]